I want to join eight 2.25" wide by .75" thick by 18" long boards (alternating boards of walnut and maple) to form a single 18" by 18" panel. I'm thinking that wood glue alone would be strong enough for that, because it would all be glued on edge grain.

However, after making the 18" by 18" panel, I need to cut it into 8 boards again (making the cuts perpendicular to the grain) and then join those together to reform the 18" by 18" panel (ending up with a panel that is made from sixty-four 2.25" squares, i.e., a checkerboard). The problem is, I'd be dealing with joining end grain to end grain at that point, and I've heard that glue isn't as effective on end grain as it is on edge grain. Would I need some form of mechanical joints (like biscuit joints maybe?) in addition to wood glue?

Here is a short video that shows what I want to do, in case my description was confusing:

Using a biscuit joiner on something like that would definitely help. I'm no expert on the "end grain vs edge grain" glue issue, but I've used a biscuit joiner to join flat boards for a keyboard tray for my desk, among other things and it's a dirty simple process

Why don't you get a thin piece of mdf and then glue the squares to the bottom board?

That's an option, but I like the idea of it just being solid hardwood and nothing else. By gluing it down to a substrate, it would then need some sort of edging/trim/molding to hide the edge of the substrate, which never looks as nice as if the edges were just solid hardwood through-and-through in the first place.

I know that the solid blocks of wood thing can be done effectively, because the Drueke company has made checkerboards like that for ~60 years, and they have always been highly regarded. I've heard that Drueke uses tongue and groove, but I don't know if that is true or not.

I built one of these back in high school. I used a biscuit joiner for most of the joints. I then added a edge piece to hide the edges. It is currently on display at my parents house otherwise I'd take a closer look and a picture because it has been a little while.

I think you'll be ok with just glue, because of the relatively large surface area, unless you need it to be super strong. biscuits are more for getting the joints lined up rather than adding strength anyway. If you need it to stand up to a beating, I would use Tongue and groove. You could make a slot in each - t moulding style - and then insert a separate piece for the Tongue.

I made a chessboard like this in junior high woodshop. Just used glue, it's still around to this day, in fact my mom uses it as a table/plant stand with a wooden base that she had. It's pretty strong. Held up over 20 years.

Like many others have said - Biscuit Joiner or Dad Tounge and Groove. But both of those require special equipment. (table saw w/ dado blades or biscuit joiner).

If you're on a tight budget, dowl rods, a hand drill and some paitence go a long way.

If you do buy a biscuit joiner - don't go cheap. The $150 Dewalt (amazon.com) is about as low as I'd go.. anything cheaper usually has a plastic fence and you'll end up redoing things a lot because of drift.

The touge & groove option is very nice, but has a lot of setup time. I'm actually setting up a second table saw as a dedicate dado table...

Your right, gluing end grain is going to be weaker, but it is still going to be a really strong joint. I would likely use dowels, but I have a Dowelmax jig, and I wouldn't trying to align mating dowel joints with a cheap jig.

I might suggest just using a spline if you're really concerned. If you you have a slot cutter you can do this with a router, and then glue a spline in the grove you cut. You can stop short of making a full length groove, and you will see no evidence of a spline on any exterior edge.

Again, unless your going to really abuse this, the end to end glue joint is still going to be really strong.

method I use for wide panels is to not plane the boards down to finish thickness at first. I then glue up "mini" panels that are not wider than can be handled on the planar I have. I then plane these mini panels down to the final thickness. You then have fewer "boards" to worry about a precise glue-up. You can now glue these mini panels together using whatever method you wish. (dowels, biscuits, splines, cawls, etc.) This cuts down on the final sanding or scraping or whatever method you use before applying finish. This works for me and I have made several tables, or cabinets requiring wider panels.